Another 'trick' that makes doing the math easier is to convert all unit into metric. Then convert values as needed back to Imperial (to compare to data sheets, etc).

23 kg-cm = 1.66 lb-ft: correct and I didn't find any problem with your other calculations.

20lb Bot and a 10% incline while accelerating will require lots of torque. There is a big difference between pushing a car (~2000lbs) on a level surface and even the slightest incline.Maybe decrease the acceleration requirement for the incline.

The gear motor you linked to includes the reduction for the torque rating. Also note that this motors stall torque is >300 kg-cm but the gear box data sheet specs a MAX momentary torque of only 150 kg-cm and does not spec the current at these torque outputs (but torque and current are close to being linear). This can allow for some additional torque as needed.

I did a little looking for what motor/gears were used for Bots of about 20lb but didn't have much luck. This was to compare what you calculated and what has worked for other people.

Maybe 20lbs is too heavy. I was hoping for a long run time (perhaps an hour) for an autonomous bot, driven by a PC, with a variety of sensors, including a Kinect and several Canon cameras. So I was erring on the high side (batteries and motors seem pretty heavy). I haven't really figured it all out but appreciate your help!

I have a little more time and studied the Specs for the Motor/gear box. Open the spec to follow along.

This is for the "IG-50 Gearhead series".

First there is a chart for gear boxes of different ratios. The one you are looking at is the 1/26 column and 24V rows.The "rated" torque and speed is 23kg-cm & 136rpm as you have been using in your calcs.

Now look at the motor graph for 24V operation (this graph has all the info needed for a full evaluation). This is just for the motor so multiply the torque by the reduction ratio.The "rated" torque (torque on the X-axis) is at the maximum efficiency, 1.3kg-cm * 26 = 33kg-cm (minus loss but ignore for now). But that is not the Maximum torque. The Maximum torque is at stall which is the far right hand end of the graph and is 6kg-cm *26 = 156kg-cm, or about 4.6 times greater. This isn't a good value to use since this also draws the highest current from the battery and the greatest heating of the motor. The I curve of the graph shows the stall current to be about 12Amps.

So now look at the peak of the PO (power) curve. The torque there is about 4.5kg-cm *26 = 117kg-cm and can be achieved if the loading requires it. These numbers plugged into the Motor part of the RMF calculator gives 18.8, much better than the 3.77 but still not quite the 61 for the 10° incline. At the max PO the motor current will be about 8Amps.

So, for a level surface use the "rated" or torque at the highest efficiency for calculations that will give the longest battery life. Then use the torque at the Max power output for when the motors are at max loading like climbing an incline.

Next is the input parameter to the RMF calculator.With the 6 inch diameter wheels the motor must run at 153rpm to go 4fps. This is the motor/gearhead's Maximum rpm with no-load. So the Bot will only go that fast down a slight incline (there are always fictional losses). I dropped the speed requirement to 3.5fps and the incline to 5° to get a require RMF of 19.3 which is really close to the 18.8 the gear motor will do at max power. This is still with a weight of 20lbs. If you can reduce the weight to 15lbs then the Bot could do a 7° incline.

On the level, incline = 0, weight = 15lbs the needed RMF = 1.2 so the Bot will move along nicely using only 0.5lb-ft (20kg-cm) of torque and drawing <2Amps.

I think that those Gearhead motors will work for you if you can reduce the weight some and accept a lower top speed.Do use speed feed-back so that the motor current can be increased if the Bot hits a bump or other resistance.

Do note the current the motor could draw (Stall current) and ensure that the motor driver circuit can supply this.

Yes that makes more sense now. It is as I expected... the motor would be be usable if I could reduce the target weight, reduce the speed, or even add two more motors. As long as I don't go uphill, that is.

<grin>

I'll have to carefully step thru the math everytime I do it, but that's not the end of the world. In fact, it is probably good for me. (argh)

I had seen the performance graphs for the motor but had not readily understood what was going on until you explained it.